Abstract
This paper is concerned with one of the basic problems in abstract interpretation, namely, for a given abstraction and a given set of concrete transformers (that express the concrete semantics of a program), how does one create the associated abstract transformers? We develop a new methodology for addressing this problem, based on a syntactically restricted language for expressing concrete transformers. We use this methodology to produce best abstract transformers for abstractions of many important data structures.
This is a preview of subscription content, log in via an institution to check access.
Preview
Unable to display preview. Download preview PDF.
Similar content being viewed by others
References
Cousot, P., Cousot, R.: Systematic design of program analysis frameworks. In: POPL (1979)
Immerman, N.: Descriptive Complexity. Springer, Heidelberg (1999)
Sagiv, M., Reps, T., Wilhelm, R.: Parametric shape analysis via 3-valued logic. Trans. on Prog. Lang. and Syst. (2002)
Loginov, A., Reps, T., Sagiv, M.: Abstraction refinement via inductive learning. In: Etessami, K., Rajamani, S.K. (eds.) CAV 2005. LNCS, vol. 3576, Springer, Heidelberg (2005)
Dong, G., Su, J.: Incremental and decremental evaluation of transitive closure by first-order queries. Inf. & Comput. 120, 101–106 (1995)
Hesse, W.: Dynamic Computational Complexity. PhD thesis, Department of Computer Science, UMass, Amherst (2003)
Rakamaric, Z., Bingham, J., Hu, A.: A better logic and decision procedure for predicate abstraction of heap-manipulating programs. Tech. Rep. TR-2006-02, Dept. of Comp. Sci. Univ. of BC, Canada (2006)
Lev-Ami, T., et al.: Constructing specialized shape analyses for uniform change. Technical Report TR-2006-11-01, Tel-Aviv Univ (2006), http://www.cs.tau.ac.il/~tla/2006/papers/TR-2006-11-01.pdf
Manevich, R., et al.: Predicate abstraction and canonical abstraction for singly-linked lists. In: Cousot, R. (ed.) VMCAI 2005. LNCS, vol. 3385, pp. 181–198. Springer, Heidelberg (2005)
Yorsh, G., Reps, T., Sagiv, M.: Symbolically computing most-precise abstract operations for shape analysis. In: Jensen, K., Podelski, A. (eds.) TACAS 2004. LNCS, vol. 2988, pp. 530–545. Springer, Heidelberg (2004)
Lev-Ami, T., Immerman, N., Sagiv, M.: Abstraction for shape analysis with fast and precise transformers. In: Ball, T., Jones, R.B. (eds.) CAV 2006. LNCS, vol. 4144, pp. 533–546. Springer, Heidelberg (2006)
Myers, E.: Efficient applicative data types. In: POPL, pp. 66–75 (1984)
Okasaki, C.: Purely Functional Data Structures. Cambridge University Press, New York (1998)
Brown, A.L.: Persistent Object Stores. Univ. of St Andrews (1989)
Edmonds, J., Johnson, E.L.: Matching, Euler tours and the chinese postman. Mathematical Programming 5, 88–124 (1973)
Hendren, L.: Parallelizing Programs with Recursive Data Structures. PhD thesis, Cornell Univ. Ithaca (1990)
Distefano, D., O’Hearn, P.W., Yang, H.: A local shape analysis based on separation logic. In: Hermanns, H., Palsberg, J. (eds.) TACAS 2006 and ETAPS 2006. LNCS, vol. 3920, pp. 287–302. Springer, Heidelberg (2006)
Reps, T., Sagiv, M., Loginov, A.: Finite differencing of logical formulas for static analysis. In: Degano, P. (ed.) ESOP 2003 and ETAPS 2003. LNCS, vol. 2618, Springer, Heidelberg (2003)
Loginov, A.: Refinement-based program verification via three-valued-logic analysis. PhD thesis, Comp. Sci. Dept. Univ. of Wisconsin, Madison (2006)
Cousot, P., Cousot, R.: Static determination of dynamic properties of recursive procedures. In: Formal Descriptions of Programming Concepts, pp. 237–277 (1978)
Rinetzky, N., Sagiv, M., Yahav, E.: Interprocedural shape analysis for cutpoint-free programs. In: Hankin, C., Siveroni, I. (eds.) SAS 2005. LNCS, vol. 3672, pp. 284–302. Springer, Heidelberg (2005)
Nelson, G.: Verifying reachability invariants of linked structures. In: POPL, pp. 38–47 (1983)
Møller, A., Schwartzbach, M.I.: The pointer assertion logic engine. In: PLDI, pp. 221–231(2001)
Lahiri, S.K., Qadeer, S.: Verifying properties of well-founded linked lists. In: POPL (2006)
Lev-Ami, T., et al.: Simulating reachability using first-order logic with applications to verification of linked data structures. In: Nieuwenhuis, R. (ed.) Automated Deduction – CADE-20. LNCS (LNAI), vol. 3632, pp. 99–115. Springer, Heidelberg (2005)
Ball, T., Rajamani, S.K.: Automatically validating temporal safety properties of interfaces. In: Dwyer, M.B. (ed.) Model Checking Software. LNCS, vol. 2057, pp. 103–122. Springer, Heidelberg (2001)
Henzinger, T.A., et al.: Software verification with BLAST. In: Ball, T., Rajamani, S.K. (eds.) Model Checking Software. LNCS, vol. 2648, pp. 235–239. Springer, Heidelberg (2003)
Reps, T., Sagiv, M., Yorsh, G.: Symbolic implementation of the best transformer. In: Steffen, B., Levi, G. (eds.) VMCAI 2004. LNCS, vol. 2937, Springer, Heidelberg (2004)
Rabin, M.: Decidability of second-order theories and automata on infinite trees. Trans. Amer. Math. Soc. 141, 1–35 (1969)
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 2007 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Lev-Ami, T., Sagiv, M., Immerman, N., Reps, T. (2007). Constructing Specialized Shape Analyses for Uniform Change. In: Cook, B., Podelski, A. (eds) Verification, Model Checking, and Abstract Interpretation. VMCAI 2007. Lecture Notes in Computer Science, vol 4349. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-69738-1_16
Download citation
DOI: https://doi.org/10.1007/978-3-540-69738-1_16
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-69735-0
Online ISBN: 978-3-540-69738-1
eBook Packages: Computer ScienceComputer Science (R0)